Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Atoms

Nonlinear Dynamics in Isotropic and Anisotropic Magneto-Optical Traps

Fernando Haas, Luiz Gustavo Ferreira Soares

Published Aug 12, 2022• 0 citations
Publisher

Abstract

We briefly review some recent advances in the field of nonlinear dynamics of atomic clouds in magneto-optical traps. A hydrodynamical model in a three-dimensional geometry is applied and analyzed using a variational approach. A Lagrangian density is proposed in the case where thermal and multiple scattering effects are both relevant, where the confinement damping and harmonic potential are both included. For generality, a general polytropic equation of state is assumed. After adopting a Gaussian profile for the fluid density and appropriate spatial dependencies of the scalar potential and potential fluid velocity field, a set of ordinary differential equations is derived. These equations are applied to compare cylindrical and spherical geometry approximations. The results are restricted to potential flows.

DOI
10.3390/atoms10030083

Related papers

Dynamics and Stability of Axially Symmetric Atomic Clouds in Magneto-Optical Trap

Luiz Gustavo Ferreira Soares, Fernando Haas

The three-dimensional nonlinear dynamics of atomic clouds in a magneto-optical trap is analyzed in terms of a self-consistent fluid formulation using a variational approach.A Lagrangian density is proposed in the case where thermal and multiple-scattering effects are both relevant, in addition to damping.For closure, an adiabatic equation of state is assumed.After adopting a Gaussian profile for the fluid density and appropriated spatial dependencies of the scalar potential and potential fluid velocity field, a set of ordinary differential equations is derived.The linear stability analysis and the prominent features of the associated normal modes are characterized.Unlike previous treatments found in the literature, the current analysis applies to non-spherically symmetric trapped atomic gases.In addition, the use of a variational approach for a dissipative system is a further distinctive feature of the work.The paper is restricted to potential flows.

Acta Physica Polonica A•Jun 1, 2021•1 citation

Nonlinear oscillations of ultra-cold atomic clouds in a magneto-optical trap

Luiz Gustavo Ferreira Soares, Fernando Haas

Abstract Confined atomic clouds in a magneto-optical trap can be formally interpreted as a single component trapped plasma. A hydrodynamical model in a three-dimensional geometry with radial symmetry is applied. A general polytropic equation of state is assumed. For suitable initial conditions and velocity fields, the Lagrangian variables method reduces the problem to ordinary differential equations in the limiting cases according to the prevalence of thermal or multiple-scattering (MS) effects. The thermal, pressure dominated case with adiabatic equation of state leads to a dissipative nonlinear oscillator with an inverse cubic force, in the form of a damped Pinney equation. An accurate approximate analytic solution derived from Kuzmak–Luke perturbation theory allows the assessment of the fully nonlinear dynamics. The applicability conditions of the two regimes are discussed. The intermediate case where both thermal and MS effects are equally relevant is also analytically studied.

Physica Scripta•Jul 25, 2019•6 citations

Polytropic equilibrium and normal modes in cold atomic traps

Hugo Terças, José Tito Mendonça

The compressibility limit of a cold gas confined in a magneto-optical trap due to multiple scattering of light is a long-standing problem. This scattering mechanism induces long-range interactions in the system, which are responsible for the occurrence of plasma-like phenomena. In the present paper, we investigate the importance of the long-range character of the mediated atom-atom interaction in the equilibrium and dynamical features of a magneto-optical trap. Making use of a hydrodynamical formulation, we derive a generalized Lane-Emden equation modeling the polytropic equilibrium of a magneto-optical trap, allowing us to describe the crossover between the two limiting cases: temperature-dominated and multiple-scattering-dominated traps. The normal collective modes of the system are also computed.

arXiv:1305.4678•Physical Review A•Aug 9, 2013•15 citations

Satellite rings and normal modes in rotating clouds of ultra cold atoms

João D. Rodrigues, José Tito Mendonça, Rodrigues, J. A.

The multiple scattering of light in a gas of ultra cold atoms is responsible for many exciting features observed in magneto-optical traps including the collective behavior forced by a Coulomb like potential. This field also induces plasma like phenomena in the cloud which allows the treatment of the system as a one component trapped plasma. With a fluid description and casting the thermodynamical behavior in the form of a polytropic equation of state we investigate the equilibrium profiles of rotating clouds and its dependence on the experiment characteristics. Numerical solutions predict the formation of stable orbital modes both in rotating and non rotating clouds. We also investigate the normal modes on such rotating systems.

arXiv:1406.6098•Jun 23, 2014•0 citations

Collective oscillations in ultracold atomic gas

José Tito Mendonça, Robin Kaiser, Hugo Terças +1 more

Using both fluid and kinetic descriptions, with repulsive forces between nearby atoms included, we discuss the basic oscillations and waves of a cloud of ultracold atoms confined in a magneto-optical trap. The existence of a hybrid mode, with properties similar to both plasma and acoustic waves, is described in detail. Tonks-Dattner resonances for confined hybrid modes in a spherical cloud are discussed, and the prediction of a nonlinear coupling between the dipole resonance and the hybrid modes is considered. Landau damping processes and quasilinear diffusion in velocity space are also discussed.

arXiv:0912.4420•Physical Review A•Jul 11, 2008•59 citations

Enhancement of Phase Space Density by Increasing Trap Anisotropy in a Magneto-Optical Trap with a Large Number of Atoms

Mukund Vengalattore, Richard Conroy, Mara Goff Prentiss

The phase space density of dense, cylindrical clouds of atoms in a 2D magneto-optic trap is investigated. For a large number of trapped atoms (>10(8)), the density of a spherical cloud is limited by photon reabsorption. However, as the atom cloud is deformed to reduce the radial optical density, the temperature of the atoms decreases due to the suppression of multiple scattering leading to an increase in the phase space density. A density of 2 x 10(-4) has been achieved in a magneto-optic trap containing 2 x 10(8) atoms.

Physical Review Letters•May 7, 2004•19 citations
We briefly review some recent advances in the field of nonlinear dynamics of atomic clouds in magneto-optical traps. A hydrodynamical model in a three-dimensional geometry is applied and analyzed using a variational approach. A Lagrangian density is proposed in the case where thermal and multiple scattering effects are both relevant, where the confinement damping and harmonic potential are both included. For generality, a general polytropic equation of state is assumed. After adopting a Gaussian profile for the fluid density and appropriate spatial dependencies of the scalar potential and potential fluid velocity field, a set of ordinary differential equations is derived. These equations are applied to compare cylindrical and spherical geometry approximations. The results are restricted to potential flows.
The three-dimensional nonlinear dynamics of atomic clouds in a magneto-optical trap is analyzed in terms of a self-consistent fluid formulation using a variational approach.A Lagrangian density is proposed in the case where thermal and multiple-scattering effects are both relevant, in addition to damping.For closure, an adiabatic equation of state is assumed.After adopting a Gaussian profile for the fluid density and appropriated spatial dependencies of the scalar potential and potential fluid velocity field, a set of ordinary differential equations is derived.The linear stability analysis and the prominent features of the associated normal modes are characterized.Unlike previous treatments found in the literature, the current analysis applies to non-spherically symmetric trapped atomic gases.In addition, the use of a variational approach for a dissipative system is a further distinctive feature of the work.The paper is restricted to potential flows.
Abstract Confined atomic clouds in a magneto-optical trap can be formally interpreted as a single component trapped plasma. A hydrodynamical model in a three-dimensional geometry with radial symmetry is applied. A general polytropic equation of state is assumed. For suitable initial conditions and velocity fields, the Lagrangian variables method reduces the problem to ordinary differential equations in the limiting cases according to the prevalence of thermal or multiple-scattering (MS) effects. The thermal, pressure dominated case with adiabatic equation of state leads to a dissipative nonlinear oscillator with an inverse cubic force, in the form of a damped Pinney equation. An accurate approximate analytic solution derived from Kuzmak–Luke perturbation theory allows the assessment of the fully nonlinear dynamics. The applicability conditions of the two regimes are discussed. The intermediate case where both thermal and MS effects are equally relevant is also analytically studied.
The compressibility limit of a cold gas confined in a magneto-optical trap due to multiple scattering of light is a long-standing problem. This scattering mechanism induces long-range interactions in the system, which are responsible for the occurrence of plasma-like phenomena. In the present paper, we investigate the importance of the long-range character of the mediated atom-atom interaction in the equilibrium and dynamical features of a magneto-optical trap. Making use of a hydrodynamical formulation, we derive a generalized Lane-Emden equation modeling the polytropic equilibrium of a magneto-optical trap, allowing us to describe the crossover between the two limiting cases: temperature-dominated and multiple-scattering-dominated traps. The normal collective modes of the system are also computed.
The multiple scattering of light in a gas of ultra cold atoms is responsible for many exciting features observed in magneto-optical traps including the collective behavior forced by a Coulomb like potential. This field also induces plasma like phenomena in the cloud which allows the treatment of the system as a one component trapped plasma. With a fluid description and casting the thermodynamical behavior in the form of a polytropic equation of state we investigate the equilibrium profiles of rotating clouds and its dependence on the experiment characteristics. Numerical solutions predict the formation of stable orbital modes both in rotating and non rotating clouds. We also investigate the normal modes on such rotating systems.
Using both fluid and kinetic descriptions, with repulsive forces between nearby atoms included, we discuss the basic oscillations and waves of a cloud of ultracold atoms confined in a magneto-optical trap. The existence of a hybrid mode, with properties similar to both plasma and acoustic waves, is described in detail. Tonks-Dattner resonances for confined hybrid modes in a spherical cloud are discussed, and the prediction of a nonlinear coupling between the dipole resonance and the hybrid modes is considered. Landau damping processes and quasilinear diffusion in velocity space are also discussed.
The phase space density of dense, cylindrical clouds of atoms in a 2D magneto-optic trap is investigated. For a large number of trapped atoms (>10(8)), the density of a spherical cloud is limited by photon reabsorption. However, as the atom cloud is deformed to reduce the radial optical density, the temperature of the atoms decreases due to the suppression of multiple scattering leading to an increase in the phase space density. A density of 2 x 10(-4) has been achieved in a magneto-optic trap containing 2 x 10(8) atoms.